FIG. 1 shows a scheme of a common method of delivering an orthopaedic paste from a container to a designated spot (bone cavity) through a thin tube. In general, the orthopaedic paste, which is a liquid-solid two-phase mixture stored in a container or reservoir, is intended to be transported through a thin tube into a designated spot in a bone structure, tissue or organ of a diseased subject. Conventionally used is a tapered cone-cylinder design which connects the container and the thin tube (syringe), wherein a driving force is applied for orthopaedic paste delivery. For this one-step, direct forced-filling method, the liquid and powder of the orthopaedic paste would tend to separate upon the exertion of the force during the filling process. The underlying physics is explained below.
Generally speaking, the speed of delivery is slow for the method illustrated in FIG. 1. The physical condition occurring in the container throughout the filling process can be described using a static equilibrium concept. The internal pressure developed is approximately equal to the applied force divided by the surface area of the back plate, namely, F/A. This pressure (P) is almost uniformly distributed everywhere except around the exit region of the container, i.e. the region near to the thin tube, where the pressure drops drastically to the ambient pressure (P0) of the designated spot, as shown in FIG. 2. This locally developed pressure gradient around the junction of the container and the tube forms the major mechanism that drives the fluid portion of the orthopaedic paste mixture out of the tiny orifice of the container. This can be illustrated by the incompressible Navier-Stokes equation of motion for a fluid flow,
                              ρ          ⁢                                    ∂              u                                      ∂              t                                      ︸            unsteady        +                            ρ          ⁢                                          ⁢          u          ⁢                                    ∂              u                                      ∂              x                                      +                  ρ          ⁢                                          ⁢          v          ⁢                                    ∂              u                                      ∂              y                                                  ︸        convection              =            -                                    ∂            p                                ∂            x                                    ︸                      pressure            gradient                                +                            μ          ⁡                      (                                                                                ∂                    2                                    ⁢                  u                                                  ∂                                      x                    2                                                              +                                                                    ∂                    2                                    ⁢                  u                                                  ∂                                      y                    2                                                                        )                          ︸                    viscous        effects            In which, ρ, u, v, p and μ are respectively the density, velocity components, pressure and viscosity of the fluid, and (x, y, t) are the Cartesian and time coordinates. The orthopaedic paste delivery motion is in general very slow so the unsteady and convection terms can be neglected, resulting in a balance of the pressure gradient and the viscous terms. In other words, the locally developed pressure gradient drives the fluid motion by overcoming the internal or wall friction as the fluid is ejected out. Owing to the large solid-liquid density ratio, the speed of the fluid usually exceeds that of the solid particles, causing the separation of the orthopaedic paste constituents. The fluid part of the orthopaedic paste will continuously flow out of the container because of the continuity characteristic of the flow motion. Nevertheless, the solid part of the orthopaedic paste experiences different physical mechanism as the force is applied. In the beginning, a diluted orthopaedic paste is ejected because more liquid than solid part is compressed out of the container. The remaining orthopaedic paste gets drier during the pressurization period. The small exit area prohibits the dried solid particles from moving quickly out of the container. Except for the initial powder that drifts out of the container with the carrier liquid, the remainder powder of the orthopaedic paste will be closely packed or interlocked together, resulting in a static equilibrium chunk due to the loss of fluidity. This liquid-solid separation mechanism explains why the one-step, direct forced-filling device often fails as a satisfactory orthopaedic paste delivery injector, especially for a minimally invasive surgical procedure.